In many technical fields, linearization of nonlinear circuitry is used to compensate for unwanted effects caused by the nonlinear behavior of the nonlinear circuitry. One possibility to linearize nonlinear circuitry is to predistort the signal input into the nonlinear circuitry to ensure that the output signal of the nonlinear circuitry is, in the ideal case, linearly related to the input signal of the predistorter.
Power amplifiers are used in wireline and wireless communications systems for transferring high-rate data signals from a transmitter to a receiver. Power amplifiers are highly cost intensive during production and also during operation. Therefore, it is desirable to operate power amplifiers in a most efficient way. As the efficiency of a power amplifier increases with nonlinearity, power amplifiers are typically driven in the nonlinear region. This leads to spectral regrowth and intermodulation distortion in the amplified signal band. These effects increase the bit error rate at the receiver and cause unacceptably high co-channel interference.
As a countermeasure to decrease the unwanted effects of nonlinearity, a predistorter may be employed to predistort the signal input to the power amplifier. Signal predistortion allows creation of low-price transmitter devices fulfilling given spectral masks for the transmission signal even though the power amplifier is driven in the nonlinear region.
It is known to use models (i.e. model networks) to approximately reproduce the nonlinear behavior of the power amplifier or, generally speaking, the nonlinear circuitry. These models may be used for simulation purposes, for instance to perform a bit error rate simulation. They may also be used for the purpose of minimizing the unwanted effects caused by the nonlinear behavior of the nonlinear circuitry.
Typically, nonlinear circuitry is modeled by a network comprising two static nonlinearities called amplitude-to-amplitude modulation conversion (AM/AM-conversion) and amplitude-to-phase modulation conversion (AM/PM-conversion). The AM/AM-conversion maps an input signal amplitude into an output signal amplitude, which may, for instance, be represented by a series expansion around the input signal amplitude. Analogously, the AM/PM-conversion maps an input signal amplitude into an output signal phase, which may equally be represented by a series expansion around the input signal amplitude. Generally, both static nonlinearities are purely dependent on the input signal magnitude. Identifying the nonlinear circuitry means to determine these two static nonlinearities—i.e. the coefficients of the series expansions in case the nonlinearities are expressed by series. Conventionally, this may be accomplished by simple two-tone or single-tone measurements. In these measurements, the power of the input signal to the nonlinear circuitry is varied and the power and the phase difference of the fundamentals at the output of the nonlinear circuitry are recorded.
Dynamic effects, also known as memory effects, are another problem encountered in nonlinear circuitries. Memory effects in power amplifiers typically show up as a non-symmetrical spectrum around the carrier at the output of the power amplifier. They are caused by thermal or electro-thermal processes in the power amplifier. As the term “memory effects” indicates, there is a dependency not only on the present value, e.g. sample, but also on previous values, e.g. samples, of the input signal.
Conventional concepts based on static AM/AM-conversion and AM/PM-conversion cannot model the dynamic or memory behavior of the power amplifier. However, the compensation of memory effects is especially important for radio frequency wideband applications.
From a theoretical point of view, it is possible to model such dynamic or memory effects by identifying the nonlinear circuitry by means of adaptive algorithms, for instance LMS (least means squares), RLS (recursive least squares). However, this requires in general a costly measurement system comprising a complex signal generator, analog-to-digital converters, a digital signal processor etc. Compared to the AM/AM and AM/PM measurements, which may be carried out by a simple network analyzer using a one-tone or two-tone input signal according to the conventional approach. The use of adaptive algorithms involves significantly higher computational efforts and system requirements.